Calculate the arithmetic mean diameter D̅_g for the -4- to + 200-mesh fractions of the material analyzed in Table 28.1. How does  D̅_g differ qualitatively from the volume mean diameter D̅_v?

Table 28.1

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TABLE 28.1 Screen analysis Mesh 468WM功循环8608129M 35 65 Pan Screen opening D. mum 3.327 2.362 1.651 1.168 0.833 0.589 0417 0.295 0.208 0.147 0.104 0.074 Mass fraction retained, x 0.0000 0.0251 0.1250 0.3207 0.2570 0.1590 0.0538 0.0210 0.0102 0.0077 0.0058 0.0041 0.0031 0.0075 Average particle diameter in increment, D, mm pis 4.013 2.845 2.007 1.409 1.001 0.711 0.503 0.356 0.252 0.178 0.126 0.089 0.037 Cumulative fraction smaller than D 1.0000 0.9749 0.8499 0.5292 0.2722 0.1132 0.0594 0.0384 0.0282 0.0205 0.0147 0.0106 0.0075 0.0000